In the second half of the dissertation, we investigate the problem of vortex trapping in cyclically coupled Bose-Josephson junctions. Starting with N independent BECs we couple the condensates through Josephson links and allow the system to reach a stable circulation by adding a dissipative term in our semiclassical equations of motion. The central question we address is what is the probability to trap a vortex with winding number m . Our numerical simulations reveal that the final distribution of winding numbers is narrower than the initial distribution of total phases, indicating an increased probability for no-vortex configurations. Specifically, the final width of the distribution of winding numbers for N sites scales as lambdaNalpha, where alpha = 0.47 +/- 0.01 and lambda < 0.67 (value predicted for the initial distribution). The actual value of lambda is found to depend on the strength of dissipation. The nonlinearity of the problem also manifests itself in the result that it is possible to obtain a non-zero circulation starting with zero total phase around the loop.